Electrophoresis is a process for separation of charged species based on different mobilities of these species in electric field. The mobilities depend on electrophoresis medium, electric field strength and characteristics of ions themselves, including net surface charge, size and shape. Small species, like metal ions, as well as large species such as viruses have been separated by electrophoretic techniques. However, electrophoresis is currently used mostly for separation of biological macromolecules, including proteins, nucleic acids and their derivatives. The process is usually carried out by forcing the molecules to migrate through an aqueous gel as the electrophoresis medium. The gels may be composed of natural or synthetic polymers. Agarose is the most widely used natural material and polyacrylamide gels represent the most common synthetic matrix. The gels are run essentially in two types of electrophoretic units, including vertical and horizontal ones. In horizontal units the contact between the electrodes and the gel may be established directly or by means of wicks. Alternatively, the gel may be immersed in a buffer which serves as a conductive medium between electrodes and the gel. This format is known as submerged gel electrophoresis and it is the simplest to operate. Submerged gel electrophoresis is widely used for analysis of nucleic acids and agarose gels are the mostly used matrix.
A new synthetic matrix has been introduced for analysis of proteins and nucleic acids by Kozulic et al (U.S. patent application Ser. No. 328,123, Analytical Biochemistry 163 (1987) 506-512 and Analytical Biochemistry 170 (1988) 478-484). The matrix is based on an acrylic monomer, N-acryloyl-tris(hydroxymethyl)aminomethane (NAT). The poly(NAT) gels were found to be more porous than polyacrylamide gels but less porous than agarose gels. The gels were particularly suitable for separation of DNA molecules in size range from about 50 to a few thousand base pairs. However, as described in Kozulic (PCT/EP 92/00368), which is incorporated herein by reference, it was noticed that resolution of DNA in the poly(NAT) gels run in the submerged gel electrophoresis mode was never as good as in the vertical format. Subsequently, it was surprisingly observed that separated DNA bands in the submerged gel were bent, that is declined from the vertical axis. Such bending is detrimental for resolution because on a gel record, made by a camera positioned above the gel, the separated bands appear broad and diffuse. The cause of this bending was related mostly to ionic compositions of the gel and electrophoresis buffer. The bending could be eliminated or greatly reduced by adjustment of the ionic composition of the gel, as disclosed in the above cited document. The adjustment needed to be done each time after a considerable change in total monomer concentration, electrophoresis buffer or gel dimensions. Since these three variables are often changed in a research laboratory to improve resolution over a certain size range, it is apparent that a great amount of work would be saved if there were gels giving good DNA resolution in the range of up to a few thousand base pairs without being hampered by bending of bands at different gel concentrations and dimensions.
Agarose gels comprising about 0.6 to 1 percent polymer are suitable for separation of DNA molecules in size range from a few thousand to a few tens of thousand base pairs. The size range can be extended to several million base pairs by pulsed field electrophoresis (Cantor et al. Ann. Rev. Biophys. Biophys. Chem. 17 (1988) 287-304). Smaller DNA molecules require higher agarose concentrations for good resolution, as generally known in prior art. However, more concentrated agarose gels are difficult to prepare due to a high viscosity of agarose solutions. Furthermore, visualization of separated bands is difficult due to gel opacity. Derivatization of hydroxyl groups of agarose, as disclosed in U.S. Pat. No. 3,956,273 to Guisely, reduces viscosity of agarose solutions as well as gel opacity. Such hydroxyethylated agarose derivatives are commercially available products known under the trade name SeaPlaque and NuSieve (FMC Corporation). NuSieve agarose is typically used at polymer concentrations from about 2 to 8% and improved resolution of small DNA in this agarose has been reported (Dumais and Nochumson, BioTechniques, 5 (1987) 62). However, separated DNA bands were bent, although to a lesser degree than in poly(NAT) gels, also in NuSieve agarose gels containing as little as 4% of polymer (Kozulic, PCT/EP 92/00368). The bending could be reduced by adjustment of ionic composition of the gel, but as noted above it would be preferable to have a gel which does not require the adjustment.
The bending effect described was influenced by several factors but it was related mostly to difference in conductivity between the electrophoresis buffer and the gel immersed in that buffer. This difference in conductivity is caused by resistance of gel polymers to migration of buffer ions. The resistance, and therefore the difference in conductivity, may be presumably reduced by lowering the polymer concentration of the gel. However, there are many reports in prior art showing that lowering of polymer concentration compromises resolution of smaller biomolecules. For example, optimal resolution of small DNA molecules requires an increase of derivatized agarose concentration to up to 8-9% polymer dry weight (Dumais and Nochumson, BioTechniques, 5 (1987) 62). It should also be noted that improved resolution of proteins is achievable by first partially depolymerizing agarose and then preparing a gel having the polymer content of around 5-6% (Nochumson et al, PCT/US90/00184).
The belief that a gel of high polymer concentration is necessary for resolution of small biomolecules is supported by a theory based on the extended Ogston model of gel electrophoresis. This model considers a gel as a random network of fibers and states that the electrophoretic mobility of a macromolecule is proportional to the volume fraction of the pores of the gel that the macromolecule can enter (Rodbard and Chrambach, Proc. Natl. Acad. Sci. USA'65 (1970) 907-977 and Tietz, Adv. Electrophoresis 2 (1988) 109-169). The model also postulates that there is no contact between migrating molecules and gel fibers. The measured electrophoretic mobility, .mu., can be related to the free mobility in solution, .mu..sub.o, of a migrating molecule with radius R, as well as to the gel percentage T, total length of the gel fibers, 1', and the fiber radius, r: EQU log .mu.=log .mu..sub.o -.pi.1'(r+R).sup.2 T.times.10.sup.-16 ( 1)
or EQU log .mu.=log .mu..sub.o -K.sub.r T (2)
where the retardation coefficient, K.sub.r, is defined as EQU K.sub.r =.pi.1'(r+R).sup.2 .times.10.sup.-16 ( 3)
Separation of two DNA fragments a and b can be written as .DELTA..mu.=.mu..sub.a -.mu..sub.b =.mu..sub.oa e.sup.-KraT -.mu..sub.ob e.sup.-KrbT. Since the free mobility .mu..sub.o of all DNA molecules is equal (Olivera et al., Biopolymers 2, (1964) 245-257) and maximal separation occurs when d(.DELTA..mu.)/dT=0, gel concentration T giving optimal resolution is: EQU T=1n(Kra/Krb)/(Kra-Krb) (4)
This equation corresponds to equation 25 of Rodbard and Chrambach (Proc. Natl. Acad. Sci. 65 (1970) 970-977). From that equation it follows that as Kra decreases, that is size of DNA fragment a becomes smaller, the gel concentration T necessary for resolution of fragments a and b increases. As noted above, however, when a gel of high polymer concentration is run in the submerged electrophoresis mode, separated bands are bent. Accordingly, from the prior art it seemed impossible to achieve optimal resolution by submerged gel electrophoresis without necessary adjustment of gel ionic composition in order to control the bending of separated bands.
The extended Ogston model teaches that very small ions are also retarded in a gel because even when radius R of an ion is zero, retardation coefficient is higher than zero (equation 1). However, from that equation it is not possible to predict at which minimal gel concentration, if at any, resistance to migration of buffer ions is so small that the difference in gel and buffer conductivity does not significantly affect the bending of bands. Experiments were designed in an attempt to find out whether there is such a gel comprising synthetic polymers, since resolution of macromolecules of small size in low percentage agarose gels is known to be inferior. In practice, the lowest workable concentration of a synthetic gel is determined by its mechanical stability which in turn depends mostly on polymerization efficiency of a starting monomer solution of a low concentration. This is true for acrylamide as well as many other hydrophilic and amphiphatic gels disclosed in (Kozulic and Heimgartner, U.S. patent applications Ser. Nos. 293,840 and 696,696), which are incorporated herein by reference. The lowest practical gel concentration is in most cases around 4%. Since in 4% gels bending of bands was still noticeable (Kozulic, PCT/EP 92/00368), it appeared important to find a way for preparation of gels of even lower percentage. Most gels in prior art were polymerized in presence of a cross-linker having two vinyl double bonds but in some of them the cross-linker was a polymer with plurality of double bonds. That cross-linker was an agarose polymer substituted with allyl glycidyl ether (U.S. Pat. No. 4,504,641 to Nochumson), which is known as Acryl Aide.RTM. (FMC Corporation). Since a mechanically more stable, low percentage gel was desirable, in an attempt to obtain such a gel the Acryl Aide.RTM. agarose polymer was cross-linked through its hydroxyl groups prior to copolymerization. It was reasoned that a single large and branched cross-linked vinyl-agarose polymer will cross-link during polymerization many chains formed from the polymerizing monomer and thus improve mechanical stability of the matrix and resolution of small biomolecules. In an initial experiment, 6% poly(NAT) gels were polymerized with different amounts of the cross-linked vinyl-agarose. Transparency and mechanical strength of the resulting gels looked standard. During electrophoresis migration rate of the bromphenol blue tracking dye was normal. However, totally unexpectedly it was observed that resolution of DNA molecules was progressively lost as the amount of the cross-linked vinyl-agarose increased and at a certain cross-linker concentration there was no resolution at all. Surprisingly, the resolution was lost even when DNA fragments migrated essentially the same distance as in the control gel. At higher cross-linker concentrations the loss of resolution was accompanied by reduced migration rates. The loss of resolution occurred first in the low molecular weight range.
The above experimental data appeared to be of limited practical importance but they were a clue that lead to development of a new model for electrophoretic migration of macromolecules in gels. The model is described herein as follows. A gel is regarded as a block comprising randomly distributed polymer chains and water. The polymer chains have different motional freedom along their length. Regions of high motional freedom are separated by spots of low motional freedom, which correspond to cross-linking points in synthetic gels. There are no pores of any finite shape or size in transparent gels. Accordingly, there is no defined space or volume a macromolecule can enter before it begins to migrate in electric field. Once it starts migrating, the macromolecule pushes the polymer chains and thus creates the space it occupies. The macromolecules move along their path in discrete steps and in each step they pass through one gel layer. The gel layer is defined as a gel cross-section perpendicular to direction of migrating molecules. A gel layer is thicker than radius of the polymer chain but thinner than radius or length of the migrating macromolecule. Thus, the migrating molecule may encounter a second layer before it completely passes through the first one, however, resistance to its migration is given only by the second layer. Essential to this model is the notion that there are two ways a macromolecule can pass trough a layer. Thus, it will push aside polymer chains when on its path the macromolecule encounters a region in which polymers have a high motional freedom. In this way the macromolecule will open a "door" in the layer. When on its path the macromolecule encounters an area where polymers have a low motional freedom, it deforms the layer until an opening is formed. This opening is created at places where one or more polymer chains end or where the polymer chains are less cross-linked or entangled. The macromolecule thus creates a "corridor" in the layer. Creation of a "corridor" in one layer is accompanied by dislocation of some polymer chains in at least one layer above and below. If the migrating macromolecule encounters a similar place on the next layer, it will again open a "corridor". These two "corridors" may be connected into a single one and thus the same "corridor" can span several layers.
Whether a macromolecule will predominantly open "doors" or "corridors" on its way through the layers depends entirely on the balance of two forces. The first force acting on the layer is electrokinetic and it is exercised by all macroions moving in an electric field. This force is countered by resistance of polymer chains comprising the layer. The polymer chains resist to any change in their arrangement because during gel formation they have acquired energetically the most favorable position. When magnitude of the electrokinetic force in relation to resistance of polymer chains is high, "corridors" will be predominantly formed. When the two forces are of similar magnitude, a part of the openings will be "doors" and part "corridors". When the ratio of electrokinetic force and resistance is small, then the openings in layers will be predominantly "doors".
On a time scale, formation of "doors" is faster than formation of "corridors" because the migrating molecules can faster form openings by pushing aside one or a few polymer chains than by deforming a part of gel layer consisting of many polymer chains. In case of DNA fragments, which have a constant charge to size ratio, longer fragments exercise stronger forces but they migrate slower because the openings they create are mostly "corridors". It is postulated that resolution of macromolecules is good when on their way through layers they open both "doors" and "corridors". There is little or no resolution when they open only "doors" or only "corridors", however, gel structure must be such that macromolecules are able to open "corridors". Accordingly, polymers of different layers must be connected in such a way that they can be dislocated sufficiently to open the "corridors". The "corridors" cannot be opened and there is no resolution when polymer chains of different layers are connected with a large, branched cross-linker, such as the one described above.
The new model predicts that if some molecules were to open "corridors" in most layers, they would migrate faster than those which open both "doors" and "corridors" since, as one "corridor" can span several layers, such molecules would pass through these layers in one step. In other words, in some gels larger molecules may migrate faster than smaller ones even at a low electric field strength. An example supporting the above prediction is presented herein. Thus, it was found that in an unidirectional electric field at 7 V/cm a 23 kbp DNA fragment migrated faster than a 9.4 kbp fragment in a standard 6% poly(NAT) gel cross-linked with Bis. This result cannot be explained in terms of the extended Ogston model because, according to equation 1, larger molecules always have a higher retardation coefficient and therefore migrate slower. Furthermore, the above result is not in accordance with the reptation model of DNA gel electrophoresis (Lumpkin et al, Biopolymers 24 (1985) 1573-1593), which states that resolution of DNA molecules above certain size is lost because all of them migrate with the same velocity in a homogenous electric field. Many experimental findings reported in prior art that have been difficult or impossible to explain can be accounted for by the model presented here but that is out of current scope.
In prior art faster or slower electrophoretic migration has been generally related to higher or lower gel porosity. Although the model presented herein states that in transparent gels macromolecules do not move through pores, because the pores do not exist, the terms "porosity" and "effective porosity" will be used hereinunder for the sake of easier comparison with results reported in prior art. One additional reason is that in many reports in prior art there is no reference to transparency of the gels used.
The above model was based on experimental data obtained with gels comprising synthetic polymers. In order to better corroborate the new model, it was desirable to obtain supporting results with gels comprising natural polymers. Since the cross-linked vinyl-agarose polymer was used as a gel component in the above mentioned crucial experiment, it appeared reasonable to assume that cross-linked agarose gels will exhibit a similar behavior, that is deteriorating resolution after cross-linking. It is widely known that agarose polymers dissolve at a high temperature and by cooling form gels suitable for electrophoresis. If the cross-linking reaction were carried out at a temperature where agarose polymers are still fully in solution, it was reasoned that they would cross-link in such a way that "corridors" could not open in the resulting gel, if a gel formed. To verify this hypothesis, into a 1% agarose solution epichlorhydrin and sodium hydroxide were added and the mixture incubated at 45.degree. and 65.degree. C. It was observed that control agarose solutions without the cross-linker did not solidify into a manageable gel at either of the two temperatures, but in the presence of epichlorhydrin a gel was formed at both temperatures. Surprisingly, both gels were fully transparent, in contrast to the characteristic opacity of standard 1% agarose gels. Electrophoresis of DNA fragments resulted in poor resolution in the gel cross-linked at 65.degree. C., especially in the 200-600 bp range. Unexpectedly, however, electrophoresis under the same conditions in the gel cross-linked at 45.degree. C. gave very good resolution of DNA fragments, also in the 200-600 bp range. Now that this surprising result was known, it was sensible to test other cross-linkers and cross-linking conditions. The general features of the above experiment remained constant, that is gel formation and cross-linking reaction proceeded simultaneously in a water solution of dissolved agarose. The gel was always in form of a continuous bed. Further, the cross-linkers reacted with hydroxyl groups of polymers to form ether linkages without introducing a charged group into the gel.
Several different cross-linked agarose derivatives are known in prior art. Thus, U.S. Pat. No. 3,507,851 to Ghetie discloses cross-linking of agarose particles with epichlorhydrin. U.S. Pat. No. 3,959,251 and UK Patent 1,352,613 both to Porath et al. disclose stabilization of agarose beads by cross-linking with several bifunctional reagents in the presence of a reducing agent. The resulting beads were more rigid, giving higher flow rates when packed into columns for chromatography. The processes and products of Ghetie and Porath are clearly different from those presented here. Thus, the cross-linking reaction was carried out after the gel was formed and the resulting products were in form of particles.
Cross-linked agarose gels in form of plates are also known. Thus, U.S. Pat. No. 3,860,573 to Honkanen discloses agarose gels cross-linked with a bifunctional reagent containing two equal functional groups selected from acyl chloride, sulfonyl chloride and isothiocyanate. The cross-linking reaction was carried out in an organic solvent with suspended and not dissolved agarose polymer. The reaction could not have been performed successfully in water because compounds having the said functional groups react fast with water. The bonds formed with bifunctional reagents were esters, sulfonates or thiocarbamates. Moreover, as some cross-linker molecules must have reacted through only one functional group, the other functional group hydrolyzed when the gel was brought into contact with water. This side reaction introduced charged groups, such as carboxylic and sulfonic, into the matrix. Due to above mentioned differences, the process and products of Honkanen are profoundly different from those disclosed herein.
Another process for treatment of polysaccharide gels comprises suspending or dissolving the polysaccharide gel in a solution of 2,4,6-trichloro-1,3,5-triazine, as disclosed in U.S. Pat. No. 3,956,272 to Tixier. The resulting strengthened gel may be in form of plates. Regarding the process of Tixier, it should be noted that the triazine ring of the starting cross-linker is incorporated into the agarose matrix. Moreover, each of the three cross-linker chlorine atoms had the possibility to react with either hydroxyl groups of agarose or water. Therefore some of the incorporated triazine molecules were inevitable converted to cyanuric acid derivatives, that is to compounds containing one or two hydroxyl groups at carbon atoms initially linked to chlorine. These hydroxyl groups are known to have a low pK value, and as such are charged at a high pH. In addition, each triazine ring contains three nitrogen atoms and, as a tertiary amine, triazine will be protonated at a low pH. Therefore, the cross-linking reaction of Tixier introduces into the gel a chemical group which is charged.
Honkanen and Tixier reported that their cross-linked agarose gels could be used as media for electrophoresis. Regarding properties of these matrices, Honkanen teaches that movement of large molecules (proteins) is more rapid in the cross-linked agarose, which would indicate an increase of effective porosity due to the cross-linking reaction. Tixier discloses that the treated gels had essentially the same characteristics as untreated gels with respect to sieving and resolving power. This result of Tixier is in accordance with the report of Porath (J. Chromatogr. 103 (1975) 49-62) who found that cross-linked agarose beads did not change their porosity. Accordingly, the reduced migration of large protein molecules and medium size DNA as well as dramatically improved resolution observed in the cross-linked gels disclosed herein are totally unexpected. Moreover, profound improvement in transparency of the gels of present invention is surprising, because neither Honkanen nor Tixier mention that opacity of their gels changed with the cross-linking.
In the prior art known are also electrophoresis gels comprising derivatized agarose. Thus, U.S. Pat. Nos. 3,956,273 to Guisely and 4,319,975 to Cook disclose many derivatized agarose polymers. After a derivatization reaction the polymers were purified and dried. To form a gel for electrophoresis, the dried polymer particles were dissolved in hot water and the solution cooled. Although majority of the modifying reagents were monofunctional, a bifunctional reagent could also be employed. However, Guisely teaches that the ratio of the bifunctional reagent to agarose as well as derivatization conditions must be such that the polymer chains are not cross-linked, since otherwise the resulting product could not be redissolved as required for subsequent preparation of the electrophoresis gel. Accordingly, even though Guisely and the present process use one common cross-linker, epichlorhydrin, the processes are different because in the present process the cross-linker reaction and formation of gel for electrophoresis occur simultaneously and the ratio of the cross-linker to agarose is much higher. These differences in processes resulted in different products, so that products of the present invention are, among other characteristics, water insoluble whereas the agarose gels of Guisely and Cook can be redissolved by heating.
Other ways of changing some properties of agarose gels are also known in prior art. For example, electroendosmosis can be eliminated by mixing agarose with another polysaccharide (U.S. Pat. No. 4,290,911), resolution of LDH isoenzymes can be improved by addition of an acidic polysaccharide (U.S. Pat. No. 4,321,121) and gel porosity can be continuously varied by using a salt gradient during gelation (U.S. Pat. No. 5,009,759).
The gels discussed above comprised agarose polymers. These polymers are composed of D-galactose and 3,6- anhydro-L-galactose, linked in alpha 1-4 linkages and thus forming linear polymers. Branched polysaccharide polymers are also widely known, and some of them have been employed in preparation of gels for electrophoresis. Thus, gels made of starch are one of the oldest media for electrophoresis. As disclosed in U.S. Pat. No. 4,094,832 to Soderberg, derivatized dextran polymers may also serve as a component of gels for electrophoresis. The dextran polymers were chemically modified in such a way that hydroxyl groups in glucose units were substituted for functional groups containing double bonds. Gel formation occurred by free radical polymerization when these double bonds polymerized or copolymerized with a small molecular weight monomer. Soderberg mentioned the possibility to cross-link dextran chains with a small cross-linker in order to make a gel for electrophoresis, however, this possibility was deemed unpractical because removal of the cross-linking reaction byproducts by diffusion would require months to complete. Whereas this is true for vertical slab or tube gels, removal of the byproducts is fast in gels for submerged gel electrophoresis because the top side of these gels is open and thus diffusion path is short. From Soderberg it is possible to infer that, if a practical way for removal of byproducts were found, gels composed of cross-linked dextran would be suitable for electrophoresis. However, as disclosed hereinunder, gels composed of this branched polysaccharide were found unsuitable.